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Stochastic Programming is, like Scenario Analysis, an approach where a set of given or generated (input) scenarios are considered. However, in Stochastic Programming we will consider them at once with each scenario at a certain probability and look for a solution that makes a trade-off between the scenario instances. The goal here is to find a solution that is feasible for all possible scenarios and maximizes the expected return (a defined objective). In addition, Stochastic Programming allows you to only make decisions that need to happen on the short term while postponing decisions of the future that can wait, the so-called recourse decisions (wait until more is known so a better decision can be made at that time).
Using Stochastic Programming to deal with uncertainty is very suitable for a large class of models where scenarios and their probabilities are known. Obviously, one has to realize that considering many scenarios can lead to very large problems that require lots of computer power and time to solve. Therefore, it can become very important to make a trade‐off between the number of scenarios considered (i.e. the quality of the solution) and the available resources for solving the corresponding model.
Stochastic Programming in AIMMS
AIMMS offers support for generating a stochastic LP/MIP recourse model from any given deterministic model, without the need to reformulate any of the constraint definitions. By only supplying additional attributes for selected parameters and variables, AIMMS can generate both a deterministic and stochastic model from the same symbolic formulation. Both models can even co-exist (within the same master model) and their solutions can be evaluated and compared.
Various support tools are available to easily create a scenario tree and the corresponding stochastic input data for a stochastic model. Efficient memory usage (because AIMMS only stores scenario data differences) , the availability of the Benders decomposition method, and the AIMMS update technology, assures that problems with a large number of scenarios can be solved efficiently as well.
Additional Information
- “Stochastic Programming” - AIMMS Language Reference (Chapter 19).
- Example “Inventory Control”, “Power System Expansion”, “Stochastic Programming” - AIMMS Installation.
- Section operations-research/mathematical-programming/stochastic-programming.
- http://en.wikipedia.org/wiki/Stochastic_programming.
- http://stoprog.org - Community on Stochastic Programming.
Examples
Other ways of modeling uncertainty:
- Uncertainty modeling (overview)
- Scenario Analysis
- Stochastic Programming
- Robust Optimization
